easiest method i've found:
first, save the default palette.
then create a copy of the palette with all the colours except the specific 16 you need to be using changed to something like #FF00FF or #00FF00 and save it seperately.
next, convert the source image to RGB
then convert the source image back to an indexed palette, importing the altered palette you saved earlier, this should auto-assign all the colours correctly.
lastly, import the default palette WITHOUT converting to RGB.
the first and last steps are entirely optional, but should be considered "good practice"